1. Field of the Invention
The present invention relates to key agreement protocols for transfer and authentication of encryption key.
2. Discussion of the Prior Art
To retain privacy during the exchange of information it is well known to encrypt data using a key. The key must be chosen so that the correspondents are able to encrypt and decrypt messages but such that an interceptor cannot determine the contents of the message.
In a secret key cryptographic protocol, the correspondents share a common key that in secret to them. This requires the key to be agreed upon between the correspondents and for provision to be made to maintain the secrecy of the key and provide for change of the key should the underlying security be compromised.
Public key cryptographic protocols were first proposed in 1976 by Diffie-Hellman and utilized a public key made available to all potential correspondents and a private key known only to the intended recipients. The public and private keys are related such that a message encrypted with the public key of a recipient can be readily decrypted with the private key but the private key cannot be derived from the knowledge of the plaintext, ciphertext and public key.
Key establishment is the process by which two (or more) parties establish a shared secret key, called the session key. The session key is subsequently used to achieve some cryptographic goal, such an privacy. There are two kinds of key agreement protocol; key transport, protocols in which a key is created by one party and securely transmitted to the second party; and key agreement protocols, in which both parties contribute information which jointly establish the shared secret key. The number of message exchanges required between the parties is called the number of passes. A key establishment protocol is said to provide implicit key authentication (or simply key authentication) if one party is assured that no other party aside from a specially identified second party may learn the value of the session key. The property of implicit key authentication does not necessarily mean that the second party actually possesses the session key. A key establishment protocol is said to provide key confirmation if one party is assured that a specially identified second party actually has possession of a particular session key. If the authentication is provided to both parties involved in the protocol, then the key authentication is said to be mutual if provided to only one party, the authentication is said to be unilateral.
There are various prior proposals which claim to provide implicit key authentication.
Examples include the Nyberg-Rueppel one-pass protocol and the Matsumoto-Takashima-Imai (MTI) and the Goss and Yacobi two-pass protocols for key agreement.
The prior proposals ensure that transmissions between correspondents to establish a common key are secure and that an interloper cannot retrieve the session key and decrypt the ciphertext. In this way security for sensitive transactions such as transfer of funds is provided.
For example, the MTI/A0 key agreement protocol establishes a shared secret K, known to the two correspondents, in the following manner:
1. During initial, one-time setup, key generation and publication is undertaken by selecting and publishing an appropriate system prime p and generator xcex1eZp* in a manner guaranteeing authenticity. Correspondent A selects as a long-term private key a random integer xe2x80x9caxe2x80x9d,1xe2x89xa6axe2x89xa6pxe2x88x922, and computes a long-term public key pA=xcex1x mod p. Correspondent B generates analogous keys b, pb. Correspondent A and B have access to authenticated copies of each other""s long-term public key.
2. The protocol requires the exchange of the following messages.
Axe2x86x92B: xcex1x mod pxe2x80x83xe2x80x83(1)
A←B: xcex1y mod pxe2x80x83xe2x80x83(2)
The values of x and y which are random integers selected by correspondent A and correspondent B respectively remain secure during such transmissions as it is impractical to determine the exponent even when the value of the generator xcex1 and the exponentiation is known provided of course that the system prime p is chosen sufficiently large.
3. To implement the protocol the following steps are performed each time a shared key is required between correspondents A and B.
(a) A chooses a random integer x,1xe2x89xa6xxe2x89xa6pxe2x88x922, and sends B message (1) i.e. xcex1x mod p.
(b) B chooses a random integer y,1xe2x89xa6yxe2x89xa6pxe2x88x922, and sends A message (2) i.e. xcex1y mod p.
(c) A computes the key K=(xcex1y)azBx mod p.
(d) B computes the key K=(xcex1x)bzAy mod p.
(e) Both share the key K=xcex1bx+ay.
In order to compute the key K, A must use his secret key a and the random integer x, both of which are known only to him. Similarly B must use her secret key b and random integer y to compute the session key K. Provided the secret keys a,b remain uncompromised, an interloper cannot generate a session key identical to the other correspondent. Accordingly, any ciphertext will not be decipherable by both correspondents.
As such this and related protocols have been considered satisfactory for key establishment and resistant to conventional eavesdropping or man-in-the-middle attacks.
In some circumstances it may be advantageous for an adversary to mislead one correspondent as to the true identity of the other correspondent.
In such an attack an active adversary or interloper E modifies messages exchanged between correspondents A and B, with the result that B believes that he shares a key K with E while A believes that she shares the same key K with B. Even though E does not learn the value of K the misinformation as to the identity of the correspondents may be useful.
A practical scenario where such an attack may be launched successfully is the following. Suppose that B in a bank branch and A is an account holder. Certificates are issued by the bank headquarters and within the certificate is the account information of the holder. Suppose that the protocol for electronic deposit of funds is to exchange a key with a bank branch via a mutually authenticated key agreement. Once B has authenticated the transmitting entity, encrypted funds are deposited to the account number in the certificate. If no further authentication is done in the encrypted deposit message (which might be the case to save bandwidth) then the deposit will be made to E""s account.
It is therefore an object of the present invention to provide a protocol in which the above disadvantages are obviated or mitigated.
According therefore to the present invention there is provided a method of authenticating a pair of correspondents A,B to permit exchange of information therebetween, each of said correspondents having a respective private key a,b and a public key pA,pB derived from a generator xcex1 and respective ones of said private keys a,b, said method including the steps of
i) a first of said correspondents A selecting a first random integer x and exponentiating a function f(xcex1) including said generator to a power g00 to provide a first exponentiated function f(xcex1)g00;
ii) said first correspondent A forwarding to a second correspondent B a message including said first exponentiated function f(xcex1)g00;
iii) said correspondent B selecting a second random integer y and exponentiating a function fxe2x80x2(xcex1) including said generator to a power g00 to provide a second exponentiated function fxe2x80x2(xcex1)g00;
iv) said second correspondent B constructing a session key K from information made public by said first correspondent A and information that is private to said second correspondent B, said session key also being constructible by said first correspondent A for information made public by B and information that is private to said first correspondent A;
v) said second correspondent B generating a value h of a function F[xcfx80,K] where F[xcfx80,K] denotes a cryptographic function applied conjointly to xcfx80 and K and where xcfx80 is a subset of the public information provided by B thereby to bind the values of xcfx80 and K;
vi) said second of said correspondents B forwarding a message to said first correspondent A including said second exponential function fxe2x80x2(xcex1)g00 and said value h of said cryptographic function F[xcfx80,K];
vii) said first correspondent receiving said message and computing a session key Kxe2x80x2 from information made public by said second correspondent B and private to said first correspondent A;
viii) said first correspondent A computing a value hxe2x80x2 of a cryptographic function h,hxe2x80x2 F[xcfx80,Kxe2x80x2]; and
ix) comparing said values obtained from said cryptographic functions F to confirm their correspondence.
As the session key K can only be generated using information that is private to either A or B, the binding of K with xcfx80 with the cryptographic function h prevents E from extracting K or interjecting a new value function that will correspond to that obtained by A.